This class interpolates tabulated functions with a bi-cubic spline. More...

#include <BicubicSplineInterpolation.h>

Inheritance diagram for BicubicSplineInterpolation:

Public Member Functions
	BicubicSplineInterpolation ()

	BicubicSplineInterpolation (const std::vector< Real > &x1, const std::vector< Real > &x2, const std::vector< std::vector< Real > > &y, const std::vector< Real > &yx11=std::vector< Real >(), const std::vector< Real > &yx1n=std::vector< Real >(), const std::vector< Real > &yx21=std::vector< Real >(), const std::vector< Real > &yx2n=std::vector< Real >())
	In the future, may add interface that allows necessary vector of boundary conditions to be supplied for each edge of grid; however, for now we just use natural splines at the grid boundaries.

virtual	~BicubicSplineInterpolation ()=default

void	setData (const std::vector< Real > &x1, const std::vector< Real > &x2, const std::vector< std::vector< Real > > &y, const std::vector< Real > &yx11=std::vector< Real >(), const std::vector< Real > &yx1n=std::vector< Real >(), const std::vector< Real > &yx21=std::vector< Real >(), const std::vector< Real > &yx2n=std::vector< Real >())
	Set the x1, x2 and y values, and first derivatives at the edges.

void	errorCheck ()
	Sanity checks on input data.

Real	sample (Real x1, Real x2, Real yx11=_deriv_bound, Real yx1n=_deriv_bound)
	Samples value at point (x1, x2)

void	sampleValueAndDerivatives (Real x1, Real x2, Real &y, Real &dy1, Real &dy2, Real yx11=_deriv_bound, Real yx1n=_deriv_bound, Real yx21=_deriv_bound, Real yx2n=_deriv_bound)
	Samples value and first derivatives at point (x1, x2) Use this function for speed when computing both value and derivatives, as it minimizes the amount of spline evaluation.

Real	sampleDerivative (Real x1, Real x2, unsigned int deriv_var, Real yp1=_deriv_bound, Real ypn=_deriv_bound)
	Samples first derivative at point (x1, x2)

Real	sample2ndDerivative (Real x1, Real x2, unsigned int deriv_var, Real yp1=_deriv_bound, Real ypn=_deriv_bound)
	Samples second derivative at point (x1, x2)

Real	sample (const std::vector< Real > &x, const std::vector< Real > &y, const std::vector< Real > &y2, Real x_int) const

ADReal	sample (const std::vector< Real > &x, const std::vector< Real > &y, const std::vector< Real > &y2, const ADReal &x_int) const

Real	sampleDerivative (const std::vector< Real > &x, const std::vector< Real > &y, const std::vector< Real > &y2, Real x_int) const

Real	sample2ndDerivative (const std::vector< Real > &x, const std::vector< Real > &y, const std::vector< Real > &y2, Real x_int) const

Protected Member Functions
void	constructRowSplineSecondDerivativeTable ()
	Precompute tables of row (column) spline second derivatives and store them to reduce computational demands.

void	constructColumnSplineSecondDerivativeTable ()

void	solve ()
	Calculates the tables of second derivatives.

void	constructRowSpline (Real x1, std::vector< Real > &spline_eval, std::vector< Real > &spline_second_derivs, Real yx11=_deriv_bound, Real yx1n=_deriv_bound)
	Helper functions to evaluate column splines and construct row spline for the given point.

void	constructColumnSpline (Real x2, std::vector< Real > &spline_eval, std::vector< Real > &spline_second_derivs, Real yx21=_deriv_bound, Real yx2n=_deriv_bound)
	Helper functions to evaluate row splines and construct column spline for the given point.

template<typename T >
T	sample (const std::vector< Real > &x, const std::vector< Real > &y, const std::vector< Real > &y2, const T &x_int, unsigned int klo, unsigned int khi) const
	Sample value at point x_int given the indices of the vector of dependent values that bound the point.

void	spline (const std::vector< Real > &x, const std::vector< Real > &y, std::vector< Real > &y2, Real yp1=_deriv_bound, Real ypn=_deriv_bound)
	This function calculates the second derivatives based on supplied x and y-vectors.

void	findInterval (const std::vector< Real > &x, Real x_int, unsigned int &klo, unsigned int &khi) const

template<typename T >
void	computeCoeffs (const std::vector< Real > &x, unsigned int klo, unsigned int khi, const T &x_int, Real &h, T &a, T &b) const

Protected Attributes
std::vector< Real >	_x1
	Independent values in the x1 direction.

std::vector< Real >	_x2
	Independent values in the x2 direction.

std::vector< std::vector< Real > >	_y
	The dependent values at (x1, x2) points.

std::vector< std::vector< Real > >	_y_trans
	Transpose of _y.

std::vector< Real >	_yx11
	Boundary conditions.

std::vector< Real >	_yx1n

std::vector< Real >	_yx21

std::vector< Real >	_yx2n

std::vector< std::vector< Real > >	_y2_rows
	Second derivatives.

std::vector< std::vector< Real > >	_y2_columns

std::vector< Real >	_row_spline_second_derivs
	Vectors used during sampling.

std::vector< Real >	_row_spline_eval

std::vector< Real >	_column_spline_second_derivs

std::vector< Real >	_column_spline_eval

Static Protected Attributes
static int	_file_number = 0
	File number for data dump.

static const Real	_deriv_bound = std::numeric_limits<Real>::max()

Detailed Description

This class interpolates tabulated functions with a bi-cubic spline.

Adopted from Numerical Recipes in C (section 3.6). Consistent with the terminology in Numerical Recipes, moving over a column spline means moving over the x1 coord Likewise, moving over a row spline means moving over the x2 coord

Definition at line 22 of file BicubicSplineInterpolation.h.

Constructor & Destructor Documentation

◆ BicubicSplineInterpolation() [1/2]

BicubicSplineInterpolation::BicubicSplineInterpolation ( )

Definition at line 15 of file BicubicSplineInterpolation.C.

15{}

◆ BicubicSplineInterpolation() [2/2]

BicubicSplineInterpolation::BicubicSplineInterpolation	(	const std::vector< Real > &	x1,
		const std::vector< Real > &	x2,
		const std::vector< std::vector< Real > > &	y,
		const std::vector< Real > &	yx11 = `std::vector<Real>()`,
		const std::vector< Real > &	yx1n = `std::vector<Real>()`,
		const std::vector< Real > &	yx21 = `std::vector<Real>()`,
		const std::vector< Real > &	yx2n = `std::vector<Real>()`
	)

In the future, may add interface that allows necessary vector of boundary conditions to be supplied for each edge of grid; however, for now we just use natural splines at the grid boundaries.

Definition at line 17 of file BicubicSplineInterpolation.C.

  : SplineInterpolationBase(),
    _x1(x1),
    _x2(x2),
    _y(y),
    _yx11(yx11),
    _yx1n(yx1n),
    _yx21(yx21),
    _yx2n(yx2n)
{
  auto n = _x2.size();
  _row_spline_second_derivs.resize(n);
  _column_spline_eval.resize(n);
 
  auto m = _x1.size();
  _column_spline_second_derivs.resize(m);
  _row_spline_eval.resize(m);
 
  errorCheck();
  solve();
}

◆ ~BicubicSplineInterpolation()

virtual BicubicSplineInterpolation::~BicubicSplineInterpolation ( )

virtualdefault

Member Function Documentation

◆ computeCoeffs()

template<typename T >

void SplineInterpolationBase::computeCoeffs	(	const std::vector< Real > &	x,
		unsigned int	klo,
		unsigned int	khi,
		const T &	x_int,
		Real &	h,
		T &	a,
		T &	b
	)		const

protectedinherited

Definition at line 85 of file SplineInterpolationBase.C.

{
  h = x[khi] - x[klo];
  if (h == 0)
    mooseError("The values of x must be distinct");
  a = (x[khi] - x_int) / h;
  b = (x_int - x[klo]) / h;
}

Referenced by SplineInterpolationBase::sample(), SplineInterpolationBase::sample2ndDerivative(), and SplineInterpolationBase::sampleDerivative().

◆ constructColumnSpline()

void BicubicSplineInterpolation::constructColumnSpline	(	Real	x2,
		std::vector< Real > &	spline_eval,
		std::vector< Real > &	spline_second_derivs,
		Real	yx21 = `_deriv_bound`,
		Real	yx2n = `_deriv_bound`
	)

protected

Helper functions to evaluate row splines and construct column spline for the given point.

Definition at line 278 of file BicubicSplineInterpolation.C.

{
  auto m = _x1.size();
 
  // Find the indices that bound the point x2
  unsigned int klo, khi;
  findInterval(_x2, x2, klo, khi);
 
  // Evaluate m row-splines to get y-values for column spline construction using
  // the indices above to avoid computing them for each j
  for (decltype(m) j = 0; j < m; ++j)
    _row_spline_eval[j] = SplineInterpolationBase::sample(_x2, _y[j], _y2_rows[j], x2, klo, khi);
 
  // Construct single column spline; get back the second derivatives wrt x1 coord
  // on the x1 grid points
  spline(_x1, row_spline_eval, column_spline_second_derivs, yx21, yx2n);
}

Referenced by sample(), sample2ndDerivative(), sampleDerivative(), and sampleValueAndDerivatives().

◆ constructColumnSplineSecondDerivativeTable()

void BicubicSplineInterpolation::constructColumnSplineSecondDerivativeTable ( )

protected

Definition at line 127 of file BicubicSplineInterpolation.C.

{
  auto m = _x1.size();
  auto n = _x2.size();
  _y2_columns.resize(n);
  _y_trans.resize(n);
 
  for (decltype(n) j = 0; j < n; ++j)
    _y_trans[j].resize(m);
 
  // transpose the _y values so the columns can be easily iterated over
  for (decltype(n) i = 0; i < _y.size(); ++i)
    for (decltype(n) j = 0; j < _y[0].size(); ++j)
      _y_trans[j][i] = _y[i][j];
 
  if (_yx11.empty())
    for (decltype(n) j = 0; j < n; ++j)
      spline(_x1, _y_trans[j], _y2_columns[j]);
 
  else
    for (decltype(n) j = 0; j < n; ++j)
      spline(_x1, _y_trans[j], _y2_columns[j], _yx11[j], _yx1n[j]);
}

Referenced by solve().

◆ constructRowSpline()

void BicubicSplineInterpolation::constructRowSpline	(	Real	x1,
		std::vector< Real > &	spline_eval,
		std::vector< Real > &	spline_second_derivs,
		Real	yx11 = `_deriv_bound`,
		Real	yx1n = `_deriv_bound`
	)

protected

Helper functions to evaluate column splines and construct row spline for the given point.

Definition at line 254 of file BicubicSplineInterpolation.C.

{
  auto n = _x2.size();
 
  // Find the indices that bound the point x1
  unsigned int klo, khi;
  findInterval(_x1, x1, klo, khi);
 
  // Evaluate n column-splines to get y-values for row spline construction using
  // the indices above to avoid computing them for each j
  for (decltype(n) j = 0; j < n; ++j)
    _column_spline_eval[j] =
        SplineInterpolationBase::sample(_x1, _y_trans[j], _y2_columns[j], x1, klo, khi);
 
  // Construct single row spline; get back the second derivatives wrt x2 coord
  // on the x2 grid points
  spline(_x2, column_spline_eval, row_spline_second_derivs, yx11, yx1n);
}

Referenced by sample2ndDerivative(), sampleDerivative(), and sampleValueAndDerivatives().

◆ constructRowSplineSecondDerivativeTable()

void BicubicSplineInterpolation::constructRowSplineSecondDerivativeTable ( )

protected

Precompute tables of row (column) spline second derivatives and store them to reduce computational demands.

Definition at line 112 of file BicubicSplineInterpolation.C.

{
  auto m = _x1.size();
  _y2_rows.resize(m);
 
  if (_yx21.empty())
    for (decltype(m) j = 0; j < m; ++j)
      spline(_x2, _y[j], _y2_rows[j]);
 
  else
    for (decltype(m) j = 0; j < m; ++j)
      spline(_x2, _y[j], _y2_rows[j], _yx21[j], _yx2n[j]);
}

Referenced by solve().

◆ errorCheck()

void BicubicSplineInterpolation::errorCheck ( )

Sanity checks on input data.

Definition at line 75 of file BicubicSplineInterpolation.C.

{
  auto m = _x1.size(), n = _x2.size();
 
  if (_y.size() != m)
    mooseError("y row dimension does not match the size of x1.");
  else
    for (decltype(m) i = 0; i < _y.size(); ++i)
      if (_y[i].size() != n)
        mooseError("y column dimension does not match the size of x2.");
 
  if (_yx11.empty())
    _yx11.resize(n, _deriv_bound);
  else if (_yx11.size() != n)
    mooseError("The length of the vectors holding the first derivatives of y with respect to x1 "
               "must match the length of x2.");
 
  if (_yx1n.empty())
    _yx1n.resize(n, _deriv_bound);
  else if (_yx1n.size() != n)
    mooseError("The length of the vectors holding the first derivatives of y with respect to x1 "
               "must match the length of x2.");
 
  if (_yx21.empty())
    _yx21.resize(m, _deriv_bound);
  else if (_yx21.size() != m)
    mooseError("The length of the vectors holding the first derivatives of y with respect to x2 "
               "must match the length of x1.");
 
  if (_yx2n.empty())
    _yx2n.resize(m, _deriv_bound);
  else if (_yx2n.size() != m)
    mooseError("The length of the vectors holding the first derivatives of y with respect to x2 "
               "must match the length of x1.");
}

Referenced by BicubicSplineInterpolation(), and setData().

◆ findInterval()

void SplineInterpolationBase::findInterval	(	const std::vector< Real > &	x,
		Real	x_int,
		unsigned int &	klo,
		unsigned int &	khi
	)		const

protectedinherited

Definition at line 65 of file SplineInterpolationBase.C.

{
  klo = 0;
  mooseAssert(x.size() >= 2, "You must have at least two knots to create a spline.");
  khi = x.size() - 1;
  while (khi - klo > 1)
  {
    unsigned int k = (khi + klo) >> 1;
    if (x[k] > x_int)
      khi = k;
    else
      klo = k;
  }
}

Referenced by constructColumnSpline(), constructRowSpline(), SplineInterpolationBase::sample(), SplineInterpolationBase::sample(), SplineInterpolationBase::sample2ndDerivative(), and SplineInterpolationBase::sampleDerivative().

◆ sample() [1/4]

ADReal SplineInterpolationBase::sample	(	const std::vector< Real > &	x,
		const std::vector< Real > &	y,
		const std::vector< Real > &	y2,
		const ADReal &	x_int
	)		const

inherited

Definition at line 113 of file SplineInterpolationBase.C.

{
  unsigned int klo, khi;
  findInterval(x, MetaPhysicL::raw_value(x_int), klo, khi);
 
  return sample(x, y, y2, x_int, klo, khi);
}

◆ sample() [2/4]

template<typename T >

T SplineInterpolationBase::sample	(	const std::vector< Real > &	x,
		const std::vector< Real > &	y,
		const std::vector< Real > &	y2,
		const T &	x_int,
		unsigned int	klo,
		unsigned int	khi
	)		const

protectedinherited

Sample value at point x_int given the indices of the vector of dependent values that bound the point.

This method is useful in bicubic spline interpolation, where several spline evaluations are needed to sample from a 2D point.

Definition at line 157 of file SplineInterpolationBase.C.

{
  Real h;
  T a, b;
  computeCoeffs(x, klo, khi, x_int, h, a, b);
 
  return a * y[klo] + b * y[khi] +
         ((a * a * a - a) * y2[klo] + (b * b * b - b) * y2[khi]) * (h * h) / 6.0;
}

◆ sample() [3/4]

Real SplineInterpolationBase::sample	(	const std::vector< Real > &	x,
		const std::vector< Real > &	y,
		const std::vector< Real > &	y2,
		Real	x_int
	)		const

inherited

Definition at line 101 of file SplineInterpolationBase.C.

{
  unsigned int klo, khi;
  findInterval(x, x_int, klo, khi);
 
  return sample(x, y, y2, x_int, klo, khi);
}

Referenced by constructColumnSpline(), constructRowSpline(), SplineInterpolation::sample(), SplineInterpolationBase::sample(), SplineInterpolationBase::sample(), SplineInterpolation::sample(), sample(), and sampleValueAndDerivatives().

◆ sample() [4/4]

Real BicubicSplineInterpolation::sample	(	Real	x1,
		Real	x2,
		Real	yx11 = `_deriv_bound`,
		Real	yx1n = `_deriv_bound`
	)

Samples value at point (x1, x2)

Definition at line 159 of file BicubicSplineInterpolation.C.

{
  constructColumnSpline(x2, _row_spline_eval, _column_spline_second_derivs, yx11, yx1n);
 
  // Evaluate newly constructed column spline
  return SplineInterpolationBase::sample(_x1, _row_spline_eval, _column_spline_second_derivs, x1);
}

Referenced by BicubicSplineFunction::value().

◆ sample2ndDerivative() [1/2]

Real SplineInterpolationBase::sample2ndDerivative	(	const std::vector< Real > &	x,
		const std::vector< Real > &	y,
		const std::vector< Real > &	y2,
		Real	x_int
	)		const

inherited

Definition at line 141 of file SplineInterpolationBase.C.

{
  unsigned int klo, khi;
  findInterval(x, x_int, klo, khi);
 
  Real h, a, b;
  computeCoeffs(x, klo, khi, x_int, h, a, b);
 
  return a * y2[klo] + b * y2[khi];
}

Referenced by SplineInterpolation::sample2ndDerivative(), and sample2ndDerivative().

◆ sample2ndDerivative() [2/2]

Real BicubicSplineInterpolation::sample2ndDerivative	(	Real	x1,
		Real	x2,
		unsigned int	deriv_var,
		Real	yp1 = `_deriv_bound`,
		Real	ypn = `_deriv_bound`
	)

Samples second derivative at point (x1, x2)

Definition at line 202 of file BicubicSplineInterpolation.C.

{
  // Take second derivative along x1 axis
  if (deriv_var == 1)
  {
    constructColumnSpline(x2, _row_spline_eval, _column_spline_second_derivs, yp1, ypn);
 
    // Evaluate second derivative wrt x1 of newly constructed column spline
    return SplineInterpolationBase::sample2ndDerivative(
        _x1, _row_spline_eval, _column_spline_second_derivs, x1);
  }
 
  // Take second derivative along x2 axis
  else if (deriv_var == 2)
  {
    constructRowSpline(x1, _column_spline_eval, _row_spline_second_derivs, yp1, ypn);
 
    // Evaluate second derivative wrt x2 of newly constructed row spline
    return SplineInterpolationBase::sample2ndDerivative(
        _x2, _column_spline_eval, _row_spline_second_derivs, x2);
  }
 
  else
    mooseError("deriv_var must be either 1 or 2 in BicubicSplineInterpolation");
}

Referenced by BicubicSplineFunction::secondDerivative().

◆ sampleDerivative() [1/2]

Real SplineInterpolationBase::sampleDerivative	(	const std::vector< Real > &	x,
		const std::vector< Real > &	y,
		const std::vector< Real > &	y2,
		Real	x_int
	)		const

inherited

Definition at line 125 of file SplineInterpolationBase.C.

{
  unsigned int klo, khi;
  findInterval(x, x_int, klo, khi);
 
  Real h, a, b;
  computeCoeffs(x, klo, khi, x_int, h, a, b);
 
  return (y[khi] - y[klo]) / h -
         (((3.0 * a * a - 1.0) * y2[klo] + (3.0 * b * b - 1.0) * -y2[khi]) * h / 6.0);
}

Referenced by SplineInterpolation::sampleDerivative(), sampleDerivative(), and sampleValueAndDerivatives().

◆ sampleDerivative() [2/2]

Real BicubicSplineInterpolation::sampleDerivative	(	Real	x1,
		Real	x2,
		unsigned int	deriv_var,
		Real	yp1 = `_deriv_bound`,
		Real	ypn = `_deriv_bound`
	)

Samples first derivative at point (x1, x2)

Definition at line 171 of file BicubicSplineInterpolation.C.

{
  // Take derivative along x1 axis
  if (deriv_var == 1)
  {
    constructColumnSpline(x2, _row_spline_eval, _column_spline_second_derivs, yp1, ypn);
 
    // Evaluate derivative wrt x1 of newly constructed column spline
    return SplineInterpolationBase::sampleDerivative(
        _x1, _row_spline_eval, _column_spline_second_derivs, x1);
  }
 
  // Take derivative along x2 axis
  else if (deriv_var == 2)
  {
    constructRowSpline(x1, _column_spline_eval, _row_spline_second_derivs, yp1, ypn);
 
    // Evaluate derivative wrt x2 of newly constructed row spline
    return SplineInterpolationBase::sampleDerivative(
        _x2, _column_spline_eval, _row_spline_second_derivs, x2);
  }
 
  else
    mooseError("deriv_var must be either 1 or 2 in BicubicSplineInterpolation");
}

Referenced by BicubicSplineFunction::derivative().

◆ sampleValueAndDerivatives()

void BicubicSplineInterpolation::sampleValueAndDerivatives	(	Real	x1,
		Real	x2,
		Real &	y,
		Real &	dy1,
		Real &	dy2,
		Real	yx11 = `_deriv_bound`,
		Real	yx1n = `_deriv_bound`,
		Real	yx21 = `_deriv_bound`,
		Real	yx2n = `_deriv_bound`
	)

Samples value and first derivatives at point (x1, x2) Use this function for speed when computing both value and derivatives, as it minimizes the amount of spline evaluation.

Definition at line 233 of file BicubicSplineInterpolation.C.

{
  constructColumnSpline(x2, _row_spline_eval, _column_spline_second_derivs, yx11, yx1n);
  y = SplineInterpolationBase::sample(_x1, _row_spline_eval, _column_spline_second_derivs, x1);
  dy1 = SplineInterpolationBase::sampleDerivative(
      _x1, _row_spline_eval, _column_spline_second_derivs, x1);
 
  constructRowSpline(x1, _column_spline_eval, _row_spline_second_derivs, yx21, yx2n);
  dy2 = SplineInterpolationBase::sampleDerivative(
      _x2, _column_spline_eval, _row_spline_second_derivs, x2);
}

◆ setData()

void BicubicSplineInterpolation::setData	(	const std::vector< Real > &	x1,
		const std::vector< Real > &	x2,
		const std::vector< std::vector< Real > > &	y,
		const std::vector< Real > &	yx11 = `std::vector<Real>()`,
		const std::vector< Real > &	yx1n = `std::vector<Real>()`,
		const std::vector< Real > &	yx21 = `std::vector<Real>()`,
		const std::vector< Real > &	yx2n = `std::vector<Real>()`
	)

Set the x1, x2 and y values, and first derivatives at the edges.

Definition at line 46 of file BicubicSplineInterpolation.C.

{
  _x1 = x1;
  _x2 = x2;
  _y = y;
  _yx11 = yx11;
  _yx1n = yx1n;
  _yx21 = yx21;
  _yx2n = yx2n;
 
  auto n = _x2.size();
  _row_spline_second_derivs.resize(n);
  _column_spline_eval.resize(n);
 
  auto m = _x1.size();
  _column_spline_second_derivs.resize(m);
  _row_spline_eval.resize(m);
 
  errorCheck();
  solve();
}

Referenced by BicubicSplineFunction::BicubicSplineFunction().

◆ solve()

void BicubicSplineInterpolation::solve ( )

protected

Calculates the tables of second derivatives.

Definition at line 152 of file BicubicSplineInterpolation.C.

{
  constructRowSplineSecondDerivativeTable();
  constructColumnSplineSecondDerivativeTable();
}

Referenced by BicubicSplineInterpolation(), and setData().

◆ spline()

void SplineInterpolationBase::spline	(	const std::vector< Real > &	x,
		const std::vector< Real > &	y,
		std::vector< Real > &	y2,
		Real	yp1 = `_deriv_bound`,
		Real	ypn = `_deriv_bound`
	)

protectedinherited

This function calculates the second derivatives based on supplied x and y-vectors.

Definition at line 19 of file SplineInterpolationBase.C.

{
  auto n = x.size();
  if (n < 2)
    mooseError("You must have at least two knots to create a spline.");
 
  std::vector<Real> u(n, 0.);
  y2.assign(n, 0.);
 
  if (yp1 >= 1e30)
    y2[0] = u[0] = 0.;
  else
  {
    y2[0] = -0.5;
    u[0] = (3.0 / (x[1] - x[0])) * ((y[1] - y[0]) / (x[1] - x[0]) - yp1);
  }
  // decomposition of tri-diagonal algorithm (y2 and u are used for temporary storage)
  for (decltype(n) i = 1; i < n - 1; i++)
  {
    Real sig = (x[i] - x[i - 1]) / (x[i + 1] - x[i - 1]);
    Real p = sig * y2[i - 1] + 2.0;
    y2[i] = (sig - 1.0) / p;
    u[i] = (y[i + 1] - y[i]) / (x[i + 1] - x[i]) - (y[i] - y[i - 1]) / (x[i] - x[i - 1]);
    u[i] = (6.0 * u[i] / (x[i + 1] - x[i - 1]) - sig * u[i - 1]) / p;
  }
 
  Real qn, un;
  if (ypn >= 1e30)
    qn = un = 0.;
  else
  {
    qn = 0.5;
    un = (3.0 / (x[n - 1] - x[n - 2])) * (ypn - (y[n - 1] - y[n - 2]) / (x[n - 1] - x[n - 2]));
  }
 
  y2[n - 1] = (un - qn * u[n - 2]) / (qn * y2[n - 2] + 1.);
  // back substitution
  for (auto k = n - 1; k >= 1; k--)
    y2[k - 1] = y2[k - 1] * y2[k] + u[k - 1];
}

Referenced by constructColumnSpline(), constructColumnSplineSecondDerivativeTable(), constructRowSpline(), constructRowSplineSecondDerivativeTable(), and SplineInterpolation::solve().

Member Data Documentation

◆ _column_spline_eval

std::vector<Real> BicubicSplineInterpolation::_column_spline_eval

protected

Definition at line 118 of file BicubicSplineInterpolation.h.

Referenced by BicubicSplineInterpolation(), constructRowSpline(), sample2ndDerivative(), sampleDerivative(), sampleValueAndDerivatives(), and setData().

◆ _column_spline_second_derivs

std::vector<Real> BicubicSplineInterpolation::_column_spline_second_derivs

protected

Definition at line 117 of file BicubicSplineInterpolation.h.

Referenced by BicubicSplineInterpolation(), sample(), sample2ndDerivative(), sampleDerivative(), sampleValueAndDerivatives(), and setData().

◆ _deriv_bound

const Real SplineInterpolationBase::_deriv_bound = std::numeric_limits<Real>::max()

staticprotectedinherited

Definition at line 79 of file SplineInterpolationBase.h.

Referenced by errorCheck().

◆ _file_number

int BicubicSplineInterpolation::_file_number = 0

staticprotected

File number for data dump.

Definition at line 153 of file BicubicSplineInterpolation.h.

◆ _row_spline_eval

std::vector<Real> BicubicSplineInterpolation::_row_spline_eval

protected

Definition at line 116 of file BicubicSplineInterpolation.h.

Referenced by BicubicSplineInterpolation(), constructColumnSpline(), sample(), sample2ndDerivative(), sampleDerivative(), sampleValueAndDerivatives(), and setData().

◆ _row_spline_second_derivs

std::vector<Real> BicubicSplineInterpolation::_row_spline_second_derivs

protected

Vectors used during sampling.

Definition at line 115 of file BicubicSplineInterpolation.h.

Referenced by BicubicSplineInterpolation(), sample2ndDerivative(), sampleDerivative(), sampleValueAndDerivatives(), and setData().

◆ _x1

std::vector<Real> BicubicSplineInterpolation::_x1

protected

Independent values in the x1 direction.

Definition at line 91 of file BicubicSplineInterpolation.h.

Referenced by BicubicSplineInterpolation(), constructColumnSpline(), constructColumnSplineSecondDerivativeTable(), constructRowSpline(), constructRowSplineSecondDerivativeTable(), errorCheck(), sample(), sample2ndDerivative(), sampleDerivative(), sampleValueAndDerivatives(), and setData().

◆ _x2

std::vector<Real> BicubicSplineInterpolation::_x2

protected

Independent values in the x2 direction.

Definition at line 93 of file BicubicSplineInterpolation.h.

Referenced by BicubicSplineInterpolation(), constructColumnSpline(), constructColumnSplineSecondDerivativeTable(), constructRowSpline(), constructRowSplineSecondDerivativeTable(), errorCheck(), sample2ndDerivative(), sampleDerivative(), sampleValueAndDerivatives(), and setData().

◆ _y

std::vector<std::vector<Real> > BicubicSplineInterpolation::_y

protected

The dependent values at (x1, x2) points.

Definition at line 95 of file BicubicSplineInterpolation.h.

Referenced by constructColumnSpline(), constructColumnSplineSecondDerivativeTable(), constructRowSplineSecondDerivativeTable(), errorCheck(), and setData().

◆ _y2_columns

std::vector<std::vector<Real> > BicubicSplineInterpolation::_y2_columns

protected

Definition at line 112 of file BicubicSplineInterpolation.h.

Referenced by constructColumnSplineSecondDerivativeTable(), and constructRowSpline().

◆ _y2_rows

std::vector<std::vector<Real> > BicubicSplineInterpolation::_y2_rows

protected

Second derivatives.

Definition at line 111 of file BicubicSplineInterpolation.h.

Referenced by constructColumnSpline(), and constructRowSplineSecondDerivativeTable().

◆ _y_trans

std::vector<std::vector<Real> > BicubicSplineInterpolation::_y_trans

protected

Transpose of _y.

Definition at line 97 of file BicubicSplineInterpolation.h.

Referenced by constructColumnSplineSecondDerivativeTable(), and constructRowSpline().

◆ _yx11

std::vector<Real> BicubicSplineInterpolation::_yx11

protected

Boundary conditions.

The first index indicates the coordinate the derivative is with respect to. The second index indicates the grid index, e.g. 1 is the lower bound, and n is the upper bound

Definition at line 105 of file BicubicSplineInterpolation.h.

Referenced by constructColumnSplineSecondDerivativeTable(), errorCheck(), and setData().

◆ _yx1n

std::vector<Real> BicubicSplineInterpolation::_yx1n

protected

Definition at line 106 of file BicubicSplineInterpolation.h.

Referenced by constructColumnSplineSecondDerivativeTable(), errorCheck(), and setData().

◆ _yx21

std::vector<Real> BicubicSplineInterpolation::_yx21

protected

Definition at line 107 of file BicubicSplineInterpolation.h.

Referenced by constructRowSplineSecondDerivativeTable(), errorCheck(), and setData().

◆ _yx2n

std::vector<Real> BicubicSplineInterpolation::_yx2n

protected

Definition at line 108 of file BicubicSplineInterpolation.h.

Referenced by constructRowSplineSecondDerivativeTable(), errorCheck(), and setData().

The documentation for this class was generated from the following files:

include/utils/BicubicSplineInterpolation.h
src/utils/BicubicSplineInterpolation.C

Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ BicubicSplineInterpolation() [1/2]

◆ BicubicSplineInterpolation() [2/2]

◆ ~BicubicSplineInterpolation()

Member Function Documentation

◆ computeCoeffs()

◆ constructColumnSpline()

◆ constructColumnSplineSecondDerivativeTable()

◆ constructRowSpline()

◆ constructRowSplineSecondDerivativeTable()

◆ errorCheck()

◆ findInterval()

◆ sample() [1/4]

◆ sample() [2/4]

◆ sample() [3/4]

◆ sample() [4/4]

◆ sample2ndDerivative() [1/2]

◆ sample2ndDerivative() [2/2]

◆ sampleDerivative() [1/2]

◆ sampleDerivative() [2/2]

◆ sampleValueAndDerivatives()

◆ setData()

◆ solve()

◆ spline()

Member Data Documentation

◆ _column_spline_eval

◆ _column_spline_second_derivs

◆ _deriv_bound

◆ _file_number

◆ _row_spline_eval

◆ _row_spline_second_derivs

◆ _x1

◆ _x2

◆ _y

◆ _y2_columns

◆ _y2_rows

◆ _y_trans

◆ _yx11

◆ _yx1n

◆ _yx21

◆ _yx2n